Problem: Simplify the following expression: $ x = \dfrac{k - 4}{k + 7} - \dfrac{1}{2} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2}{2}$ $ \dfrac{k - 4}{k + 7} \times \dfrac{2}{2} = \dfrac{2k - 8}{2k + 14} $ Multiply the second expression by $\dfrac{k + 7}{k + 7}$ $ \dfrac{1}{2} \times \dfrac{k + 7}{k + 7} = \dfrac{k + 7}{2k + 14} $ Therefore $ x = \dfrac{2k - 8}{2k + 14} - \dfrac{k + 7}{2k + 14} $ Now the expressions have the same denominator we can simply subtract the numerators: $x = \dfrac{2k - 8 - (k + 7) }{2k + 14} $ Distribute the negative sign: $x = \dfrac{2k - 8 - k - 7}{2k + 14}$ $x = \dfrac{k - 15}{2k + 14}$